On the category of Lie nn-algebroids

Lie nn-algebroids and Lie infinity algebroids are usually thought of exclusively in supergeometric or algebraic terms. In this work, we apply the higher derived brackets construction to obtain a geometric description of Lie nn-algebroids by means of brackets and anchors. Moreover, we provide a geometric description of morphisms of Lie nn-algebroids over different bases, give an explicit formula for the Chevalley–Eilenberg differential of a Lienn-algebroid, compare the categories of Lie nn-algebroids and NQ-manifolds, and prove some conjectures of Sheng and Zhu  [10].